The use of IWTs (integral wavelet transforms) and inverse IWTs is well established in MRA (multi-resolution analysis) processing of 1-D (one dimensional) digital data, such as audio signals, and/or 2-D (two dimensional) digital data, such as image data. A special feature of IWTs and inverse IWTs is that they provide narrow windowing of short duration high frequency data while also providing wide windowing of long duration low frequency data. This is generally described in Chui, C. K., "An Introduction to Wavelets", Academic Press, Boston, Mass., 1992, which is hereby incorporated by reference. The following discussion provides examples of how IWTs and inverse IWTs have been implemented in the past.